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Harmonic Mean
Statistics - Harmonic Mean
What is Harmonic Mean?
Harmonic Mean is also a mathematical average but is pmited in its apppcation. It is generally used to find average of variables that are expressed as a ratio of two different measuring units e. g. speed is measured in km/hr or miles/sec etc.
Weighted Harmonic Mean
Formula
$H.M. = frac{W}{sum (frac{W}{X})}$
Where −
${H.M.}$ = Harmonic Mean
${W}$ = Weight
${X}$ = Variable value
Example
Problem Statement:
Find the weighted H.M. of the items 4, 7,12,19,25 with weights 1, 2,1,1,1 respectively.
Solution:
| ${X}$ | ${W}$ | $frac{W}{X}$ |
|---|---|---|
| 4 | 1 | 0.2500 |
| 7 | 2 | 0.2857 |
| 12 | 1 | 0.0833 |
| 19 | 1 | 0.0526 |
| 25 | 1 | 0.0400 |
| $sum W$ | $sum frac{W}{X}$= 0.7116 |
Based on the above mentioned formula, Harmonic Mean $G.M.$ will be:
$H.M. = frac{W}{sum (frac{W}{X})} \[7pt] , = frac{6}{0.7116} \[7pt] , = 8.4317 $∴ Weighted H.M = 8.4317
We re going to discuss methods to compute the Harmonic Mean for three types of series:
Inspanidual Data Series
When data is given on inspanidual basis. Following is an example of inspanidual series:
| Items | 5 | 10 | 20 | 30 | 40 | 50 | 60 | 70 |
|---|
Discrete Data Series
When data is given alongwith their frequencies. Following is an example of discrete series:
| Items | 5 | 10 | 20 | 30 | 40 | 50 | 60 | 70 |
|---|---|---|---|---|---|---|---|---|
| Frequency | 2 | 5 | 1 | 3 | 12 | 0 | 5 | 7 |
Continuous Data Series
When data is given based on ranges alongwith their frequencies. Following is an example of continous series:
| Items | 0-5 | 5-10 | 10-20 | 20-30 | 30-40 |
|---|---|---|---|---|---|
| Frequency | 2 | 5 | 1 | 3 | 12 |